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Slide Rules

Cylindrical Slide Rules

Writing a logarithmic scale in a spiral that is then imprinted around the outside of a cylinder allows instrument makers to lengthen the scale. Since a logarithmic scale only needs to run to 10 twice to include all possible results from adding or subtracting two logarithmic numbers, this means that the distance between the points on the scale may be increased. When any two numbers on the scale are further apart, the user may read a fractional position between these numbers (expressed as a decimal) to a finer level of granularity. For example, on a 10" linear slide rule, results generally may be calculated to only three significant figures (0.123, 1.23, 12.3, 123, 1230, and so on). A cylindrical slide rule may provide results of up to seven significant digits (0.1234567, 1.234567, 12.34567, 123.4567, 1234.567, and so on).

On the other hand, cylindrical slide rules were typically about twice as expensive to produce as linear slide rules, and the provenances for the objects on this page indeed suggest that, in the main, only corporate and government offices could afford them. A number of the objects in this category were received with instruction manuals and advertising pamphlets, which may be viewed in the Index by Makers & Retailers. The collection includes multiple examples for several of the objects, as the 23 items below represent only eight different slide rules, half developed in Europe and half invented by Americans. The cylindrical slide rule by Edwin Thacher, a Pennsylvania railroad bridge designer, also illustrates the 19th-century shift in production from Europe to the United States, as originally William Ford Stanley's London firm made the entire instrument. Then, Keuffel and Esser of New York City began constructing the wooden drum and brass and wood stand while continuing to import the scales printed on paper and pasted around the drum. Finally, K&E developed its own dividing engine for printing the scales and henceforth manufactured the entire instrument in the United States.

This rule consists of an outer wooden cylinder that both slides up and down and rotates. Two brass rings lined with felt are inside this cylinder. The cylinder is covered with paper marked with a single spiral logarithmic scale graduated into 7,250 parts and having a length, according to the maker, of 500 inches (nearly 42 feet). This length permitted computations up to four or five significant digits.

Inside the outer cylinder is a longer wooden cylinder, covered with paper marked with decimal, conversion, and sine tables. A solid mahogany handle is at one end. A brass index is screwed to the top of the handle. A second, longer brass index is screwed to the mahogany base and marked with a scale of equal parts used in finding logarithms. A third, removable, nickel-plated brass cylinder is inside the instrument and attached to the base. There is no case.

The tables on the middle cylinder include: decimal equivalents of feet and inches in feet; decimal equivalents of quarter weights and pounds in hundredweights; decimal equivalents of ounces and pounds in fractions of a pound; decimal equivalents of pounds, shillings, and pence in fractions of a pound; decimal equivalents of pence in shillings; days of the year as a fraction of the year; decimal equivalents of subunits of an acre; properties of various metals and woods; decimal equivalents of minutes of a degree in degrees; the Birmingham wire gauge; various conversion factors (mostly for weights and measures); and natural sines.

The outer, sliding cylinder is marked near the top: FULLERS SPIRAL SLIDE RULE. Near the bottom is marked: ENTD. STATS. HALL; STANLEY, Maker, LONDON. The bottom is stamped: 1389. The top of the long brass index is engraved: 1389 (/) 1901. According to Wayne Feely, these numbers indicate the instrument has serial number 1389 and was made by Stanley in 1901. A white celluloid tag affixed to the handle reads: KEUFFEL & ESSER CO. (/) ST. LOUIS. CHICAGO. (/) NEW YORK. (/) U.S.A. In the 1901 Keuffel & Esser catalog, Fuller's Spiral Slide Rule is listed as Model 4015 and priced at $30.00.

See also MA*311958, 1998.0046.01, and MA*316575.

References: Wayne E. Feely, "The Fuller Spiral Scale Slide Rule," Chronicle of the Early American Industries Association 50, no. 3 (1997): 93–98; Catalogue of Keuffel & Esser (New York, 1901), 290; James J. Fenton, "Fuller's Calculating Slide-Rule," Transactions and Proceedings of the Royal Society of Victoria 22 (1886): 57–61; Dieter von Jezierski, Slide Rules: A Journey Through Three Centuries, trans. Rodger Shepherd (Mendham, N.J.: Astragal Press, 2000), 42–43; George Fuller, Instructions for the Use of the Fuller Calculator (London: W. F. Stanley & Co., Ltd., [about 1950]), http://www.mccoys-kecatalogs.com/KEManuals/4015/4015.htm. An 1879 first edition of the instructions manual was received with the instrument and is stored in the accession file.